Dokuwiki is my choice.

1. There is no database, all flat file just in folders, love this. When my infrastructure is down, at least I can still get to my notes so I can fix it

2. Its markdown but not exact markdown, but no DB makes it worth that pain. You can for sure edit via vi, finding the files is a little harder though

3. I use search both in the gui and with a cli tool, and both work great!

I love the interface of wikijs and easy to run with docker-compose.

https://js.wiki/

Check out Pepperminty Wiki, it's about as simple as they get.

TiddlyWiki is my jam. Everything in one single html file (though can be a little more complex than that if needed).

https://tiddlywiki.com/

I recently created WipWiki to solve 3 of your 4 points, search could be easily added though if your interested in collaborating.

You can play around with the UI here: https://wiki.wip2p.com

QOwnNotes (https://github.com/pbek/QOwnNotes) is what I use

single binary install, and if you already have md files you just point it at them and go... if you don't like it (even after you edited a few of your files with it), well your files are still there, still in markdown

give it a shot :)

For an actual wiki that does all the things a wiki is supposed to, it’s hard to beat dokuwiki.

If you want a desktop wiki (as opposed to a web app) you might like Zim.